MathCastle
Groups and FieldsEasyHomomorphisms and Isomorphisms

Homomorphisms and Isomorphisms · Easy problem

The map φ:Z9→Z9\varphi: \mathbb Z_9 \to \mathbb Z_9, φ(k)=4k mod 9\varphi(k) = 4k \bmod 9, is an isomorphism. Which k∈{0,1,…,8}k \in \{0,1,\dots,8\} satisfies φ(k)=1\varphi(k) = 1?